I find it really hard to apply makeup on over BP... I'm not sure if it's because of the BP itself or because I use a lot of moisturiser if I've applied BP but it's probably both of these things, combined with dryness / flakes from BP that make applying makeup difficult...
On days where I need to (or want to) where makeup, I either apply a tiny amount of BP, apply BP just to active, or go without BP. If my skin is really dry and flaky then I'll sometimes exfoliate (carefully and gently) with a face towel. Normally I wouldn't recommend this because it could cause unwanted irritation for a lot of people - but surprisingly this has worked pretty well for me and hasn't seemed to aggravate my acne. I then use moisturiser and let that absorb completely (maybe go have breakfast) and then apply a little more moisturiser or a bit of primer (maybe apply extra moisturiser to the drier / scabbed areas). I let that absorb / dry and use my (knock-off) beauty blender to apply liquid foundation and then a tiny brush to apply concealer (just dabbing it on and blending a little - gently though so not to 'disturb' flakes). I think clean fingers would work well too (just patting and gently blending) though I haven't tried that since starting BP again.
I think it's a good idea to just pat / press the makeup on and avoid buffing etc into the skin with a brush or rubbing with fingers, as that's just going to 'disturb' the flakes / dryness and have it show up more. I don't use a powder or powder foundation because to me I think it would make me skin feel drier or show up flakes more - but that's just me guessing - I haven't actually tried it.
I really don't know a lot about makeup and I'm just going off what my experiences have been so hopefully some more people reply because I'd love to hear more tips for this too!